Find the area of the region between the parabola `x = y^2 - 6y` and the line ` x = -y`

Explanation

`x=y^{2}` and the line `y=x-6`


area in QI+ area in QIV



`|int_{-2}^{3}[(y+6)-y^{2}] d y| `


`=1|frac{y^{2}}{2}+6 y-y^{3} / 3|_{-2}^{3} `


`=|frac{9}{2}-frac{4}{2}+6(5)-[frac{27}{3}+8 / 3]|`


`|frac{5}{2}+30-[frac{35}{3}]|=frac{15+180-70}{6}=frac{125}{6} text { sq units. }`